If Vanessa gives Rael $32, the amount of money she has will be 30% of his. If Rael gives Vanessa $122, he will have the same amount of money as her. How much money did each of them have?
(a) Rael
(b) Vanessa
|
Case 1 |
Case 2 |
|
Rael |
Vanessa |
Rael |
Vanessa |
Before |
10 u - 32 |
3 u + 32 |
6.5 u + 122 |
6.5 u - 122 |
Change |
+ 32 |
- 32 |
- 122 |
+ 122 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Vanessa gives to Rael, there is an internal transfer of money from Vanessa to Rael. The total amount that both have remains the same.
In Case 2, when Rael gives to Vanessa, there is an internal transfer of money from Rael to Vanessa. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Vanessa and Rael have
= 10 u + 3 u
= 13 u
Amount that Vanessa and Rael each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Rael has at first is the same in Case 1 and Case 2.
10 u - 32 = 6.5 u + 122
10 u - 6.5 u = 122 + 32
3.5 u = 154
1 u = 154 ÷ 3.5 = 44
Amount that Rael has
= 10 u - 32
= 10 x 44 - 32
= 440 - 32
= $408
(b)
Amount that Vanessa has
= 3 u + 32
= 3 x 44 + 32
= 132 + 32
= $164
Answer(s): (a) $408; (b) $164